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When a voltage greater than the breakdown voltage is applied to an insulating medium, it will typically experience breakdown. Breakdown occurs when the insulating properties of the medium are compromised, leading to a sudden increase in current flow and the formation of a conductive path. This can result in the medium getting punctured or cracked due to arcing or electrical discharge.

So, the correct option is:

It will get punctured or cracked

The potential gradient across the material of low permittivity is greater than across the material of high permittivity. 

The potential gradient (\( E \)) is inversely proportional to the permittivity (\( \varepsilon \)) of the material, according to the relationship:

\[ E = \dfrac{V}{d} \cdot \dfrac{1}{\varepsilon} \]

Where:
- \( V \) is the potential difference,
- \( d \) is the separation distance between the plates,
- \( \varepsilon \) is the permittivity of the material.

Since \( \varepsilon \) is in the denominator, a lower permittivity results in a higher potential gradient.

So, the correct option is:

greater

Once a capacitor charges to the voltage of the battery in a DC circuit, the current in the circuit becomes zero. 

So, the correct option is:

is zero for any capacitance value

Among the options provided, ceramics typically have the highest value of dielectric constant (relative permittivity) compared to glass, vacuum, and oil. Ceramics often have high dielectric constants, making them suitable for various capacitor applications.

So, the correct option is:

Ceramics

The capacitance of a capacitor remains unaffected by changes in the thickness of the plates. 

The capacitance \( C \) of a parallel plate capacitor is given by the formula:

\[ C = \dfrac{{\varepsilon_0 \cdot \varepsilon_r \cdot A}}{{d}} \]

Where:
- \( \varepsilon_0 \) is the vacuum permittivity,
- \( \varepsilon_r \) is the relative permittivity (dielectric constant) of the material between the plates,
- \( A \) is the area of overlap of the plates,
- \( d \) is the separation distance between the plates.

As you can see from the formula, the capacitance depends on the area of the plates (\( A \)), the permittivity of the dielectric (\( \varepsilon_r \)), and the distance between the plates (\( d \)). The thickness of the plates does not affect the capacitance.

So, the correct option is:

Thickness of the plates

Among the options provided, electric potential is not a vector. 

Linear momentum, angular momentum, and electric field are all vector quantities because they have both magnitude and direction associated with them. However, electric potential (voltage) is a scalar quantity that represents the potential energy per unit charge at a point in space. It does not have direction; it only has magnitude.

So, the correct option is:

Electric potential

The direction of the electric field due to a positive charge is away from the charge. 

Electric field lines radiate outward from positive charges and terminate on negative charges. 

So, the correct option is:

away from the charge

The ability of charged bodies to exert force on one another is attributed to the existence of an electric field. 

Electric fields surround charged particles and extend throughout space, exerting forces on other charged particles within the field. Charged bodies experience forces due to the interactions of their electric fields.

So, the correct option is:

electric field

If a capacitor shows charging when tested with an ohmmeter, but the final resistance reading is appreciably less than normal, it suggests that the capacitor is leaky. In other words, it is not holding its charge properly, and some current is leaking through the dielectric material.

So, the correct option is:

leaky

Ceramic capacitors are commonly used in transistor circuits. They are known for their stability, reliability, and ability to provide high capacitance values in a small package, making them suitable for various applications in electronic circuits.

So, the correct option is:

Ceramic